{"status": "success", "data": {"description_md": "Let $P(x)$ be the unique polynomial of minimal degree with the following properties:\n\n- $P(x)$ has a leading coefficient $1$,\n- $1$ is a root of $P(x)-1$,\n- $2$ is a root of $P(x-2)$,\n- $3$ is a root of $P(3x)$, and\n- $4$ is a root of $4P(x)$.\n\nThe roots of $P(x)$ are integers, with one exception. The root that is not an integer can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers. What is $m+n$?\n\n$\\textbf{(A) }41\\qquad\\textbf{(B) }43\\qquad\\textbf{(C) }45\\qquad\\textbf{(D) }47\\qquad\\textbf{(E) }49$", "description_html": "

Let P(x) be the unique polynomial of minimal degree with the following properties:

The roots of P(x) are integers, with one exception. The root that is not an integer can be written as \\frac{m}{n}, where m and n are relatively prime integers. What is m+n?

\\textbf{(A) }41\\qquad\\textbf{(B) }43\\qquad\\textbf{(C) }45\\qquad\\textbf{(D) }47\\qquad\\textbf{(E) }49

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2023 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p22", "prev": "/problem/23_amc10A_p20"}}